On the asymptotic performance analysis of subspace DOA estimation in the presence of modeling errors:: Case of MUSIC

This paper provides a new analytic expression of the bias and RMS error (root mean square) error of the estimated direction of arrival (DOA) in the presence of modeling errors. In [1]-[5], first-order approximations of the RMS error are derived, which are accurate for small enough perturbations. However, the previously available expressions are not able to capture the behavior of the estimation algorithm into the threshold region. In order to fill this gap, we provide a second-order performance analysis, which is valid in a larger interval of modeling errors. To this end, it is shown that the DOA estimation error for each signal source can be expressed as a ratio of Hermitian forms, with a stochastic vector containing the modeling error. Then, an analytic expression for the moments of such a Hermitian forms ratio is provided. Finally, a closed-form expression for the performance (bias and RMS error) is derived. Simulation results indicate that the new result is accurate into the region where the algorithm breaks down.